We have cognition measures at age 8 and age 15, but they are from different instruments. But we thought we would try to fit a multilevel model anyways. We standardised the year 8 and standardised year 15 and reshaped them into long form. We have a person level predictor called genetics (a categorical variable with 3 categories in this particular analysis) and a time level predictor called age (representing age 8 or age 15, also as the variable for time). We have made the slope of age random. We hope to test the interaction between genetic and age on the cognition.

At level 1 is time, As the cognition measures are standardised and not comparable across age 8 and age, the variances at level 1 should be near null, except for the person's rankings specific to both times (I guess). If this is the case, then meaning of the effect of level 1 time predictor, age, would be not interpretable. But do you think the variances of the slopes of age still of any meaning? I think it might represent how people move up and down in their 'yearly rankings' in the population (we use cohort data of a population).

When the model uses genotype, a level 2 variable, to explain the the variance of the slope of age, we get the gene-age interaction, a cross level interaction. But since I am not sure if the variance of the slope of age is interpretable, could I interpret the meaning of the gene-age interaction?